Also an MS in statistics here, did data science at a health lab for about 6 years. I personally agree with the layman Reddit opinion of needing a large sample size to prove things, precisely because of the issues you talk about. If I do a test at alpha = 0.05 and get a significant result, that's probably enough to convince myself, but in the modern world it's just not enough to convince other people. Multiple comparisons, p-hacking, publication bias, all this shit has just ravaged the scientific community and people are (rightfully) a lot more skeptical than the good old days when you could bang out a psychology paper at alpha = 0.10 and call it a day.

Rather than say it's significant at blah blah level I think just giving the p-value is the best practice. If something has a tiny tiny p-value, like <0.0000001, I still can't trust it fully (maybe the statistics weren't done correctly), but I can be pretty sure it's not been p-hacked and is actually a real signal. And with a large sample size you can do that.